Linear model fit error

clear all;
close all;
clc;
x1 = [7 8 7 8 7 8 7 8 7 8 7 8 7 8 7 8 6.5 8.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5];
x2 = [12 12 12 12 12 12 12 12 20 20 20 20 20 20 20 20 16 16 16 16 16 16 8 24 16 16 16];
x3 = [25 19 19 25 19 25 25 19 19 25 25 19 25 19 19 25 22 22 22 22 22 22 22 22 16 28 22];
y = [147 273.2 244.4 176.5 243.5 203.1 169.9 247.6 253.1 164.1 127.9 250.1 124.9 235.5 197.2 166.7 189.6 170.9 199.7 233.1 216 218.5 223.2 229.5 244.2 37.12 228.8];
x = [x1 x2 x3];
Mdl = fitlm(x,y,'polyijk');
disp(Mdl);

I am trying to get the estimates for the beta parameters of an equation by using least square method. There are three variables. I am trying to fit the data and do it but I get this error message.

Error in fitlm (line 121)

model = LinearModel.fit(X,varargin{:});

Error in leastsquare (line 9)

Mdl = fitlm(x,y,'polyijk');

Any tips are appreciated, thank you

Answer 1

[Jeff Miller]

Use the transpose operator on x1, x2, x3 and y so that these are column variables, like this for x1:

x1 = [7 8 7 8 7 8 7 8 7 8 7 8 7 8 7 8 6.5 8.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5]';

Also, you are supposed to replace the 'ijk' with numbers in polyijk. For example, 'poly222' would give you a quadratic term for each predictor.

[Noe Sanchez]

Ok, I will try this tomorrow morning and will let you know if it works. Thank you very much

Answer 2

[dpb]

x1 = [7 8 7 8 7 8 7 8 7 8 7 8 7 8 7 8 6.5 8.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5 7.5].';
x2 = [12 12 12 12 12 12 12 12 20 20 20 20 20 20 20 20 16 16 16 16 16 16 8 24 16 16 16].';
x3 = [25 19 19 25 19 25 25 19 19 25 25 19 25 19 19 25 22 22 22 22 22 22 22 22 16 28 22].';
y = [147 273.2 244.4 176.5 243.5 203.1 169.9 247.6 253.1 164.1 127.9 250.1 124.9 235.5 197.2 166.7 189.6 170.9 199.7 233.1 216 218.5 223.2 229.5 244.2 37.12 228.8];
x = [x1 x2 x3];
Mdl = fitlm(x,y,'poly111')
Mdl = 
Linear regression model:
    y ~ 1 + x1 + x2 + x3

Estimated Coefficients:
                   Estimate      SE       tStat       pValue  
                   ________    ______    _______    __________
    (Intercept)     451.82     98.208     4.6007    0.00012594
    x1              14.292     11.423     1.2511       0.22346
    x2             -1.8031     1.4279    -1.2628       0.21931
    x3             -14.981     1.9038    -7.8691    5.6852e-08

Number of observations: 27, Error degrees of freedom: 23
Root Mean Squared Error: 28
R-squared: 0.739,  Adjusted R-Squared: 0.705
F-statistic vs. constant model: 21.7, p-value = 6.77e-07
>>